Post-Buckling Of Elastic Beams Under Point Space-Constraint

As one of the widely used types of components in the mechanical and civil engineering, the post-buckling behavior of beams has always been an important research topic in stability. Usually, beams are not independent existence. The contact may occur between beams and other components because of post-buckling deflection, and the constraint force arises at the contact region. It is called space-constraint. When the deflection reaches the gap value and contact with the point space-constraint, the constraint force arises. It's necessary to study the equilibrium paths and configurations of the beams depending on the point constraint force. Based on the geometrically nonlinear theory for extensional Euler-Bernoulli beams, post-buckling behavior of elastic beams with a middle point space-constraint under axially compress or hygrothermal loading were studied in this thesis. It is difficult to obtain analytical solutions because of the strong nonlinearity of equations, shooting method is used to get the numerical solution of equations. Content consists of three parts:1,Based on the geometrically nonlinear theory for extensional beams, establishing set of nonlinear governing equations of extensional Euler-Bernoulli beam under axial mechanical loading and uniform heat loading, which including seven basic unknown variables. Establishing the numerical procedure of these nonlinear boundary value problems using shooting method.2,Using the basic governing equations and the numerical method, analysis the post-buckling behavior of axially compressed elastic beams with a middle point space-constraint under axial mechanical loading. For clamped-clamped beam and hinged-hinged beam, equilibrium paths and configurations of the beams under the middle point space-constraint were presented. Emphatically analyze the change law of equilibrium path, binding force and end displacement depending on constraint force after the middle point deflection reach the gap value.3,Post-buckling behavior of elastic beams with a middle point space-constraint under uniform hygrothermal were studied. Because the hygrothermal post-buckling behavior is caused by the axial expansion, the axial expansion rate and end axial displacement limited are the foundation of this kind of post-buckling. The numerical solutions of equations are obtained using shooting method. The moment at mid-point, binding force, axial load, the moment at end point of fixed-fixed beam and angle at the end point of pinned-pinned beam were analyzed. And the comparisons between the value of no constraint and those of point space-constraint are given. Based on the comparison of binding force under same hygrothermal with fixed-fixed and pinned-pinned, provide theoretical basis for the design of a class of damp-heat controller.